The Scottish government said it already provided "significant support" for the games sector in Scotland, handing out more than £6.75m last year.
That figure included direct support to computer games companies from Scottish Enterprise and Creative Scotland.
A spokeswoman said: "We will continue to put pressure on the UK government to implement tax breaks, which we believe is the best way enhance the competitive edge of our computer games industry on the international stage.
"Giving Scotland control of these tax levers would be the best way of ensuring we support all our key industries."
A UK Treasury spokeswoman said the government was committed to making the UK "the best place to start, finance and grow a business" and making it an attractive location for innovative industries.
Labour MSP Jenny Marra has laid a motion at Holyrood calling on the Scottish government to find extra funds to boost the games sector.
She said: "There are games hubs across the UK, but a specific Scottish government fund would send a clear signal to industry that Scotland is not only open for business - but is the place for computer game developers to set up business."